Remark 2: The optimal pilot power allocation scheme improves the ergodic achievable rate with imperfect CSI. Nevertheless, the performance improvement is achieved at the expense of the PAPR increase. More specifically, the PAPR of the pilot symbols in the optimal pilot power allocation strategy is defined by [1]}
\({\text{PAPR}_o} = \frac{{\max \left\lbrace  {{p_k}} \right\rbrace }}{{\mathbb {E}\left\lbrace  {{p_k}} \right\rbrace }} = \frac{{{p_{\max }}}}{p},\) 
